Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_148

2/148 The disk A rotates about the vertical z-axis with a constant speed \(\omega = \dot{\theta} = \pi/3\) rad/s. Simultaneously, the hinged arm OB is elevated at the constant rate \(\dot{\phi} = 2\pi/3\) rad/s. At time \(t = 0\), both \(\theta = 0\) and \(\phi = 0\). The angle \(\theta\) is measured from the fixed reference x-axis. The small sphere P slides out along the rod according to \(R = 50 + 200t^2\), where \(R\) is in millimeters and \(t\) is in seconds. Determine the magnitude of the total acceleration \(a\) of \(P\) when \(t = 1/2\) s.